Social Choice

Environmental Economics:
Social Choice
Environmental Economics: Social Choice
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Social choice
Environmental economists start by taking as given individual
preferences and ask how social or group decisions can be made.
How do individuals view the environment?
How do we aggregate all the individual opinions to create an opinion
for society as a whole?
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Individual attitudes towards the environment
Biocentrism: all living things have intrinsic value, regardless of their
instrumental value (usefulness)
Anthropocentrism: only value of environment is its intrumental value
to humans
Utilitarianism: well-being that people attain from the environment,
whether instrumental, spiritual, intrinsic
Precautionary principle: future is uncertain; therefore take actions
that minimize potential losses
Sustainability: development that meets the needs of the present
generation without compromising the ability of future generations to
meet their own needs
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Social choice from individual values
Utility function: no restriction on individual preferences
One approach to model individual utilities:
Utility of individual i : Ui (xi , e )
xi composite market good
e environmental quality
Di¤erent individuals consume di¤erent amounts of the composite
market good, but the same amount of environmental quality
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Pollution damages in utility terms (McKitrick, 2011)
Consumer’s preferences are represented by a utility function
U (x, e ) where x is a vector of consumption goods and e is the level
of emissions
Consumer faces a price vector p for x, and has income M.
Solving the utility maximization problem yields continuous demand
functions x (p, e, m )
Denote by u0 the household’s optimized utility in the absence of any
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Denote the household’s expenditure function as m (p, e, U ) = h,
showing the minimum amount h the household must spend to achieve
utility U, given prices p and pollution level e.
The Total Damages function TD is de…ned by
m (p, e, u0 ) = m (p, 0, u0 ) + TD (p, e )
TD is the amount the household would need to receive to be as well
o¤ in the presence of pollution (assuming optimal choices on x) as it
would have been in the absence of pollution.
Marginal damage:
MD (p, e, u0 ) = TDe = me
MD is continuous with respect to e, by construction
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Sample Question
Suppose a utility function is given by
U (x1 , x2 , e ) = x1α x2
where x1 and x2 are consumer goods with corresponding prices p1 , p2 ,
α + β =1 and e is pollution emissions.
Total income is denoted M.
Derive the Total and Marginal Damage functions.
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Social choice from individual values
Voting as a social choice mechanism
Unanimity/Pareto criterion
hard to fault but not possible to compare all bundles
Unanimity with accompanying side payments
possible to compare more bundles than Pareto criterion, but transfers
may not be possible/desirable in reality
Hicks (1940): if transfers could be made to acheive unanimity, then the
choice is socially desirable even if no transfer is actually made (equity
versus e¢ ciency debate)
Majority rule
possible to compare all bundles but does not take into account
intensities of preferences
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Social Welfare Function
Let W be a function that associates a single number with every
distribution of utilities in society: W (U1 , ..., UN )
If W (U1 (a) , ..., UN (a)) > W (U1 (b ) , ..., UN (b )) then a is the
socially preferred bundle over b.
Benthamite: W (U1 , ..., UN ) = ∑i θ i Ui . θ i
Egalitarian: W (U1 , ..., UN ) = ∑i Ui λ ∑i [Ui min (Ui )]
Rawlsian: W (U1 , ..., UN ) = min (Ui )
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Arrow’s Impossibility Theorem
There is no rule satisfying all of the following axioms for converting
individual preferences into a social preference ordering.
Completeness: we should be able to compare all social alternatives
Unanimity: If everyone in society prefers a to b, then society as a
whole should also prefer a to b.
Nondictatorship: No individual should always get their way
Universality: Any possible individual rankings of alternatives is
Transitivity: If a is socially preferred to b and b to c, then a should
be socially preferred to c.
Independence of irrelevant alternatives: Society’s choice between a
and b should only depend on how individuals rank a and b, without
regard to other alternatives
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Criticism of Utilitarian Perspective
Utility functions may change over time (advertising, education)
Not everyone is included in voting
Should policies be based on individual preferences?
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Mandatory Readings
Chapter 3, Kolstad
Chapter 2, McKitrick
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